Fury, who holds the WBC world heavyweight title, teased a blockbuster showdown against Ngannou on social media.
He called upon the UFC president to set up the cross-code clash, tweeting: "Who would like to see me fight this beast boxing rules UFC gloves?"
White has since shared his thoughts on a potential boxing bout between Fury and Ngannou, saying he isn't surprised by the call out.
He believes 'these boxing guys' haven't got anyone to fight hence why they are challenging MMA fighters.
Speaking after UFC Vegas 46, he said: "Listen man, these guys... None of this surprise me.
"It’s like these boxing guys need guys to fight," he added. "You know what I mean?
"And yeah, no, it doesn’t surprise me at all."
The self-proclaimed 'Gypsy King' hasn't fought since destroying Deontay Wilder last year.
He's waiting for his next assignment, with Dillian Whyte reportedly in line to challenge for the WBC championship.
A fight against Ngannou could also be on the cards, with 'The Predator' hellbent on squaring off against the undefeated British star.
He told TMZ: "It's always been down the line. This is something I'm not taking my eyes off of.
"It's gonna happen, either way. Even if, when the UFC and I finalise a deal, the boxing part has to be into it because I can't see myself retire without boxing.
"Tyson Fury, Deontay Wilder. I would like to test myself to that level. It's not the same sport, although I'm the champion, I'm in the top in this division.
"At the end of the day, it's just about like trained hands, trained punches, having a good delivery system to produce bombs and I'm sure that if I deliver my own punch, it's pretty good, I can make some damage."
Before a potential battle with Fury, Ngannou will defend his UFC heavyweight crown against UFC interim champion Ciryl Gane at UFC 270 next weekend.
Featured Image Credit: YouTube/Tyson Fury
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